Since it's just a game, you can use a simple model for drag in which the drag force is proportional to the wind speed (it's actually proportional to the square of the wind speed, but that makes everything really complicated):
\vec F_w = \alpha (\vec v_w - \vec v)
\alpha is a constant that...
Usually, linear means if f(x, t) and g(x, t) are both solutions, then so is Af + g. I think though sometimes in the context of wave mechanics and optics "linear" just means non-dispersive. Can I get some backup on that? Non-dispersive meaning the wave speed is not a function of wavelength and...
The answer is complicated. Really complicated. As in four month long fourth year university level course complicated. The whole issue of light paths and wavelength is endlessly subtle because wavelength is relative to the velocity an observer present at a point in spacetime the light goes...
Closed sets and cluster points are concerns of topology and topology is independent of the chosen metric. Saying the space is metric does not factor into topological considerations. How familiar are you with the ideas of modern topology and manifolds?
First of all, it is not an induced spin, it is an induced change in spin. The former would imply the electron had no spin to start with, which isn't true.
A laser can change an electron's spin state because the energy of an electron in a magnetic field is a function of this state. This is one...
This is actually quite a complicated problem, but let's just see here. The membrane can be modeled using a driven damped harmonic oscillator. The driving force is given by the force on the coil due to the current and magnetic field. The Lorentz force law for conductors should work for that. The...
It is easy to give a particle coordinates in space and no volume. It is done all the time in classical physics as an approximation. Something like this:
V = 0, or the particle occupies no volume. The particle's mass is m. The position is (x(t), y(t), z(t)) where x, y, and z are the 3d...
I believe the first experiment confirming some of the properties of particle spin was the Stern-Gerlach experiment. Wikipedia, with any luck, should give a good description of what happened.
Ah. You should read about the WKB approximation. And yes, a lot of the tools that quantum physicists and engineers use are numerical methods. Oh, you should also read about statistical mechanics. The theory of quantum physics is used regularly in statistical mechanics. So you could say quantum...
Spin has a mathematical description that completely explains the results of certain experiments. Thus we know exactly what spin is. Its mathematical description defines it.
Now, if you are going to ask what is "really" going on underneath the mathematical description, I have this to say...
Yes, systems can be entangled and remain a great distance from one another. Consider firing two atoms at one another. They will interact, entangle, and scatter. They will remain entangled as they separate from one another.
I don't think one could point to just one particular problem with reconciling the two theories, but if I had to, then I'd say the biggest problem is the stress-energy tensor in the Einstein field equations. It determines how spacetime is curved, but it is determined by macroscopic properties...
What I meant to say is that to understand how subatomic particles behave, you need to discard almost all analogies to the macroscopic matter everybody is already familiar with. Electrons don't "spin around pivots" like spinning balls in space. They don't have angular velocity. They don't have a...